The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings
This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2...
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my-usm-ep.475482020-10-14T08:04:30Z The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings 2017-10 Mohammed Alarifi, Najla QA1 Mathematics (General) This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| < 1: All functions f ∈ U are univalent. In the first problem, the U -radius is determined for several classes of analytic functions. These include the classes of functions f satisfying the inequality Re f (z)=g(z) > 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1k 2017-10 Thesis http://eprints.usm.my/47548/ http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik (School of Mathematical Engineering) |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
| spellingShingle |
QA1 Mathematics (General) Mohammed Alarifi, Najla The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| description |
This thesis studies geometric and analytic properties of complex-valued analytic functions and logharmonic mappings in the open unit disk D. It investigates four
research problems. As a precursor to the first, let U be the class consisting of normalized analytic functions f satisfying |(z= f (z))2 f ′(z)−1| < 1: All functions f ∈ U are univalent. In the first problem, the U -radius is determined for several classes of analytic functions. These include the classes of functions f satisfying the inequality Re f (z)=g(z) > 0; or | f (z)=g(z)−1| < 1 in D; for g belonging to a certain class of
analytic functions. In most instances, the exact U -radius are found. A recent conjecture by Obradovi´c and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. The second problem deals with the Hankel determinant of analytic functions. For a normalized analytic function f ; let z f ′(z)= f (z) or 1+z f ′′(z)= f ′(z) be subordinate to a given analytic function
φ in D. Further let F be its kth-root transform, that is, F(z) = z[f(zk)=zk]1k |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Mohammed Alarifi, Najla |
| author_facet |
Mohammed Alarifi, Najla |
| author_sort |
Mohammed Alarifi, Najla |
| title |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_short |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_full |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_fullStr |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_full_unstemmed |
The U -Radius And Hankel Determinant For Analytic Functions, And Product Of Logharmonic Mappings |
| title_sort |
u -radius and hankel determinant for analytic functions, and product of logharmonic mappings |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik (School of Mathematical Engineering) |
| publishDate |
2017 |
| url |
http://eprints.usm.my/47548/1/NAJLA%20MOHAMMED%20ALARIFI.pdf%20cut.pdf |
| _version_ |
1747821800207679488 |